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Generalized Stanley-Reisner rings and translative group actions

  • Alessio D'Ali (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)

Abstract

The Stanley-Reisner correspondence, which assigns a commutative ring to each finite simplicial complex, is a useful and well-studied bridge between commutative algebra and combinatorics. In 1987 Sergey Yuzvinsky proposed a construction that allows to see the Stanley-Reisner ring of a finite simplicial complex as the ring of global sections of a sheaf of rings on a poset. Motivated by applications in the theory of Abelian arrangements, Emanuele Delucchi and I extend Yuzvinsky's construction to the case of (possibly infinite) finite-length simplicial posets. This generalization behaves well with respect to quotients of simplicial complexes and posets by translative group actions.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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